You do have the right idea but as Homebody said, ceramic heat lamp would be a better choice to help with ambient temperature. Heat mat does nothing at all for ambient air temperature. It’s only to have a warm spot on the floor of the enclosure where the animal can retreat to. If your reading 105F in areas of the enclosure I'm sure the temperature is even higher than that directly over the heat mat. Absolutely you have to tweak the thermostat and consider alternatives for ambient air temperature.